CDM (version 1.0-0)

Data-sim: Artificial Data: DINA and DINO

Description

Artificial data: dichotomously coded fictitious answers of 400 respondents to 9 items assuming 3 underlying attributes.

Usage

data(sim.dina)
  data(sim.dino)
  data(sim.qmatrix)

concept

• sim dina
• sim dino
• sim qmatrix

format

The sim.dina and sim.dino data sets include dichotomous answers of $N=400$ respondents to $J=9$ items, thus they are $400$ times $9$ data matrices. For both data sets $K=3$ attributes are assumed to underlie the process of responding, stored in sim.qmatrix. The sim.dina data set is simulated according to the DINA condensation rule, whereas the sim.dino data set is simulated according to the DINO condensation rule. The slipping errors for the items 1 to 9 in both data sets are 0.20, 0.20, 0.20, 0.20, 0.00, 0.50, 0.50, 0.10, 0.03 and the guessing errors are 0.10, 0.125, 0.15, 0.175, 0.2, 0.225, 0.25, 0.275, 0.3. The attributes are assumed to be mastered with expected probabilities of -0.4 , 0.2, 0.6, respectively. The correlation of the attributes is 0.3 for attributes 1 and 2, 0.4 for attributes 1 and 3 and 0.1 for attributes 2 and 3.

References

Rupp, A. A., Templin, J. L. and Henson, R. A. (2010) Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.

Examples

##
## (2) examples based on dataset sim.dina
##

# DINA Model
d1 <- din(sim.dina, q.matr = sim.qmatrix, rule = "DINA",
  conv.crit = 0.01, maxit = 500, progress = TRUE)
summary(d1)

# Mixed DINA and DINO Model
d1b <- din(sim.dina, q.matr = sim.qmatrix, rule = 
  c(rep("DINA", 7), rep("DINO", 2)), conv.crit = 0.01,
  maxit = 500, progress = FALSE)
summary(d1b)

# DINO Model
d2 <- din(sim.dina, q.matr = sim.qmatrix, rule = "DINO",
  conv.crit = 0.01, maxit = 500, progress = FALSE)
summary(d2)

# Comparison of DINA and DINO estimates
lapply(list("guessing" = rbind("DINA" = d1$guess[,1],
  "DINO" = d2$guess[,1]), "slipping" = rbind("DINA" = 
  d1$slip[,1], "DINO" = d2$slip[,1])), round, 2)

# Comparison of the information criteria
c("DINA"=d1$AIC, "MIXED"=d1b$AIC, "DINO"=d2$AIC)

# following estimates:
d1$coef            # guessing and slipping parameter
d1$guess           # guessing parameter
d1$slip            # slipping parameter
d1$skill.patt      # probabilities for skills
d1$attribute.patt  # attribute pattern with probabilities
d1$subj.pattern    # pattern per subject

# posterior probabilities for every response pattern
d1$posterior       

##
## (3) examples based on dataset sim.dino
##

# DINO Estimation
d3 <- din(sim.dino, q.matr = sim.qmatrix, rule = "DINO",
  conv.crit = 0.005, progress = FALSE)

# Mixed DINA and DINO Model
d3b <- din(sim.dino, q.matr = sim.qmatrix, rule = 
  c(rep("DINA", 4), rep("DINO", 5)), conv.crit = 0.001, 
  progress = FALSE)
                        
# DINA Estimation
d4 <- din(sim.dino, q.matr = sim.qmatrix, rule = "DINA",
  conv.crit = 0.005, progress = FALSE)
            
# Comparison of DINA and DINO estimates
lapply(list("guessing" = rbind("DINO" = d3$guess[,1],
  "DINA" = d4$guess[,1]), "slipping" = rbind("DINO" = 
  d3$slip[,1], "DINA" = d4$slip[,1])), round, 2)

# Comparison of the information criteria
c("DINO"=d3$AIC, "MIXED"=d3b$AIC, "DINA"=d4$AIC)

##
## (4) example estimation with weights based on dataset sim.dina
##

# Here, a weighted maximum likelihood estimation is used 
# This could be useful for survey data.

# i.e. first 200 persons have weight 2, the other have weight 1
(weights <- c(rep(2, 200), rep(1, 200)))

d5 <- din(sim.dina, sim.qmatrix, rule = "DINA", conv.crit = 
  0.005, weights = weights, progress = FALSE)
        
# Comparison of the information criteria
c("DINA"=d1$AIC, "WEIGHTS"=d5$AIC)


##
## (5) example estimation within a Balanced Incomplete 
##     Block (BIB) Design generated on dataset sim.dina
##

# generate BIB data

# The next example shows that the din function
# works for (relatively arbitrary) missing value pattern

# Here, a missing by design is generated in the dataset dinadat.bib
sim.dina.bib <- sim.dina
sim.dina.bib[1:100, 1:3] <- NA
sim.dina.bib[101:300, 4:8] <- NA
sim.dina.bib[301:400, c(1,2,9)] <- NA


d6 <- din(sim.dina.bib, sim.qmatrix, rule = "DINA", 
  conv.crit = 0.0005, weights = weights, maxit=200)

d7 <- din(sim.dina.bib, sim.qmatrix, rule = "DINO",
  conv.crit = 0.005, weights = weights)

# Comparison of DINA and DINO estimates
lapply(list("guessing" = rbind("DINA" = d6$guess[,1],
  "DINO" = d7$guess[,1]), "slipping" = rbind("DINA" =
  d6$slip[,1], "DINO" = d7$slip[,1])), round, 2)